Giúp em zới ạ e cần gấp lém

Đáp án:

e. \(\left\{ \begin{array}{l}
y = \dfrac{{14}}{3}\\
x = \dfrac{{28}}{9}\\
z = \dfrac{{56}}{9}
\end{array} \right.\)

Giải thích các bước giải:

\(\begin{array}{l}
a.DK:x \ne \left\{ { - 7; - 5} \right\}\\
\dfrac{{2x - 3}}{{x + 5}} = \dfrac{{5 - 2x}}{{ - x - 7}}\\
 \to  - 2{x^2} - 14x + 3x + 21 = 5x + 25 - 2{x^2} - 10x\\
 \to  - 6x = 4\\
 \to x =  - \dfrac{2}{3}\\
b.DK:x \ne \left\{ { - \dfrac{5}{2};\dfrac{3}{2}} \right\}\\
\dfrac{{x - 7}}{{2x + 5}} = \dfrac{{4x - 11}}{{8x - 12}}\\
 \to 8{x^2} - 12x - 56x + 84 = 8{x^2} + 20x - 22x - 55\\
 \to  - 66x =  - 139\\
 \to x = \dfrac{{139}}{{66}}\\
c.\left\{ \begin{array}{l}
x = \dfrac{5}{3}y\\
{x^2} + {y^2} = \dfrac{1}{4}
\end{array} \right.\\
 \to \left\{ \begin{array}{l}
x = \dfrac{5}{3}y\\
\dfrac{{25}}{9}{y^2} + {y^2} = \dfrac{1}{4}
\end{array} \right.\\
 \to \left\{ \begin{array}{l}
x = \dfrac{5}{3}y\\
\dfrac{{34}}{9}{y^2} = \dfrac{1}{4}
\end{array} \right.\\
 \to \left\{ \begin{array}{l}
x = \dfrac{5}{3}y\\
{y^2} = \dfrac{9}{{136}}
\end{array} \right.\\
 \to \left[ \begin{array}{l}
y = \dfrac{{3\sqrt {34} }}{{68}}\\
y =  - \dfrac{{3\sqrt {34} }}{{68}}
\end{array} \right.\\
 \to \left[ \begin{array}{l}
x = \dfrac{{5\sqrt {34} }}{{68}}\\
x =  - \dfrac{{5\sqrt {34} }}{{68}}
\end{array} \right.\\
d.\left\{ \begin{array}{l}
x = \dfrac{1}{{12}}y\\
z = \dfrac{1}{4}y\\
\dfrac{1}{{12}}y + y + \dfrac{1}{4}y = 34
\end{array} \right.\\
 \to \left\{ \begin{array}{l}
x = \dfrac{1}{{12}}y\\
z = \dfrac{1}{4}y\\
\dfrac{4}{3}y = 34
\end{array} \right.\\
 \to \left\{ \begin{array}{l}
x = \dfrac{1}{{12}}y\\
z = \dfrac{1}{4}y\\
y = \dfrac{{51}}{2}
\end{array} \right.\\
 \to \left\{ \begin{array}{l}
x = \dfrac{{17}}{8}\\
z = \dfrac{{51}}{8}\\
y = \dfrac{{51}}{2}
\end{array} \right.\\
e.\left\{ \begin{array}{l}
x = \dfrac{2}{3}y\\
z = \dfrac{4}{3}y\\
2.\dfrac{2}{3}y - 2y + 5.\dfrac{4}{3}y = 28
\end{array} \right.\\
 \to \left\{ \begin{array}{l}
x = \dfrac{2}{3}y\\
z = \dfrac{4}{3}y\\
6y = 28
\end{array} \right.\\
 \to \left\{ \begin{array}{l}
y = \dfrac{{14}}{3}\\
x = \dfrac{{28}}{9}\\
z = \dfrac{{56}}{9}
\end{array} \right.
\end{array}\)